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A body of mass $\mathrm{m}$ is kept on a rough horizontal surface (coefficient of friction $=\mu$ ) A horizontal force is applied on the body, but it does not move. The resultant of normal reaction and the frictional force acting on the object is given by $\mathrm{F},$ where $\mathrm{F}$ is
A rough vertical board has an acceleration $‘a’$ so that a $2$ kg block pressing against it does not fall. The coefficient of friction between the block and the board should be
A block is placed on a rough horizontal plane. A time dependent horizontal force $F = Kt$ acts on the block. Here $K$ is a positive constant. Acceleration-time graph of the block is
Calculate the acceleration (In $m/s^{2}$) of the block and trolly system shown in the figure. The coefficient of kinetic friction between the trolly and the surface is $0.05 .\left( g =10\; m / s ^{2},\right.$ mass of the string is negligible and no other friction exists).
A motor cyclist moving with a velocity of $72\, km/hour$ on a flat road takes a turn on the road at a point where the radius of curvature of the road is $20$ meters. The acceleration due to gravity is $10 m/sec^2$. In order to avoid skidding, he must not bend with respect to the vertical plane by an angle greater than
An annular ring with inner and outer radii $R_{1}$ and $R_{2}$ is rolling without slipping with a uniform angular speed. The ratio of the forces experienced by the two particles situated on the inner and outer parts of the ring, $\frac{F_{1}}{F_{2}}$ is
A mass of $100\, gm$ is tied to one end of a string $2 \,m$ long. The body is revolving in a horizontal circle making a maximum of $200$ revolutions per min. The other end of the string is fixed at the centre of the circle of revolution. The maximum tension that the string can bear is .......... $N$. (approximately)